Vector Algebra: JEE Main 2021 Mathematics question

Let $\overrightarrow x$ be a vector in the plane containing vectors $\overrightarrow a = 2\widehat i - \widehat j + \widehat k$ and $\overrightarrow b = \widehat i + 2\widehat j - \widehat k$. If the vector $\overrightarrow x$ is perpendicular to $\left( {3\widehat i + 2\widehat j - \widehat k} \right)$ and its projection on $\overrightarrow a$ is ${{17\sqrt 6 } \over 2}$, then the value of $|\overrightarrow x {|^2}$ is equal to __________.